Wolfram Function Repository
Instant-use add-on functions for the Wolfram Language
Category
216 items
Evolve a 2D array of cells by randomly adding new cells at positions with certain neighborhood configurations
Return a substitution tiling
Give the antidiagonal of a matrix
Tests whether a matrix is an antidiagonal matrix
Use the arcsine law to assess the randomness of a sequence of zeros and ones
Find the area between two plane curves
Generate the axis-angle representation of a three-dimensional rotation matrix
Solve computational problems using a generic backtracking algorithm
Generate an orthonormal basis from a given 3D real vector
Simplify Bessel functions in expression
Evaluate the Bickley function
Self-delimiting number representation
Conduct a runs–based test on a sequence of zeros and ones
Efficient computation of a binomial coefficient modulo a given number
Compute the binormal surface to a curve
Apply a Boolean function to corresponding bits in integers
Compute the Björling formula
Join multiple boundaries to form a single boundary ElementMesh
Give the column-simplifying conditions for Runge–Kutta methods
Compute the weight of a Butcher tree
Get a list of terms in the Taylor series expansion of the error for Runge–Kutta methods
Give the quadrature conditions for Runge–Kutta methods
Give the row-simplifying conditions for Runge–Kutta methods
Get a list of the number of Butcher trees through a given order
Get characteristics of Butcher trees, such as the height, width, order, density and number of labelings
Get the butcher trees through a given order that are not reduced by Butcher’s quadrature or row- or column-simplifying conditions
Compute the parametrization of a canal surface
Find a canonical version of a directed hypergraph
Plot the catacaustic of a curve
Create a generalized Cayley graph from generators and relations
Get the derivative with respect to a function
Plot iterations for the 2D chaos game
Calculate the value of the second Chebyshev function ψ(x)
Calculate the value of the first Chebyshev function θ(x)
Test a sequence of zeroes and ones (or a set of random reals between 0 and 1) for equidistribution and return a p-value
Return the Christoffel symbol for a given metric
Compute the vertex chromatic number of a graph
Compute the Clausen functions
Get a cofactor of a matrix
Get the Collatz sequence starting with a given value
Compute properties of the column space of a matrix
Add a complex transformation to an image
Get the nth composite number
Switch the rows and columns of a partition
Determine whether a hypergraph is connected
Closed form of cos(2π/p) where p is a Fermat prime (3, 5, 17, 257, 65537) a la Gauss
Get the pairs of primes that differ by 4
Calculate the cumulative averages of a list
Conduct a cumulative sum-based randomness test that creates a test statistic from the maximum value that a cumulative sums random walk achieves
Compute the evolution of a cyclic tag system
Compute the Darboux vector field of a curve
Test whether the permutation list is completely scrambled
Give all the ways the numbers 1, 2, …, n can be scrambled completely
Split a list at its left-to-right maxima
Get the diagonalized matrix of a given matrix
Give all possible ways to form proper brackets
Generate a cellular automaton evolution with initial conditions chosen by a click
Compute Egyptian fractions using different methods
Given tensors and their indices, sum over repeated indices
Compute the Enneper-Weierstrass parametrization
Enumerate possible inequivalent string substitution rules with a given signature
Get the number of permutations with a given number of ascents
Find a near-minimal set of integer marks so that all integers up to a given length are represented as differences
Compute a Groebner basis and a conversion matrix from the input polynomials to the basis
Compute a reduced basis for a set of vectors, along with a unimodular matrix that converts from the vectors to the reduced basis
Evaluate the Fabius function
Get a graph representation for the factorization of an integer
Fast factorial modulo a given number
Display the Ferrers diagram of a partition with dots
Get the fibbinary sequence
Fibonacci-digit encoding for a number
Find instances of a binary operator that satisfy equational constraints
Find up to a specified number of isomorphisms between two permutation groups
Find all isomorphisms between two orderless (undirected) hypergraphs
Try to find the repetition period for nesting of a function
Find isomorphisms between two ordered (directed) hypergraphs
Find all proper k-colorings of a specified graph
Express an integer factorization as it would be seen in a factorization table
Compute and visualize the roots of fractional (noninteger) derivatives of polynomials
Get a pair of lists representing the Ferrers diagram of a partition
Construct the permutation list corresponding to the given inversion vector
Convert TensorContract expressions into an equivalent form using Dot and Tr
Count the number of ways to partition a set where the order of the subsets matters
Determine the injectivity and surjectivity of a function
Model ball trajectories in a 2D Galton board using Hertzian force laws between the ball and the pegs
Compute the Gaussian curvature of a surface
Find the error in the Gaussian quadrature approximation of a function’s integral
Get a list of abscissa-weight pairs based on the Gaussian quadrature
Create fractals by random partial jumps toward reference points
Get all representations of an even integer as the sum of two primes
Find a unimodular conversion matrix corresponding to a lattice Gramian matrix
Get k-subsets of a given set in minimum change order
Get subsets of a given set in minimum change order
Test whether an integer is a happy number
Get steps of Hofstadter's MU riddle
Get the list of lists whose entries are the hook lengths of the entries of a Young diagram
Give the index of an ordered tuple or return the ordered tuple with that index
Give the index of a subset or return the subset with that index
Generate all compositions of an integer into the specified number of parts
Counts the number of times an integer k appears within all possible ways to partition an integer n without calculating n’s integer partitions
Check whether the argument is a weakly decreasing list of positive integers
Determine the spectral decomposition of an integer in a modular number system
Compute and plot the approximation to the integral of a function of two variables on a rectangle using different methods and partition types
Check if a list is the inversion vector of a permutation written as a list
Compute a periodogram for data from unevenly spaced intervals
Simulate the Ising model using a cellular automata
Determine whether two orderless (undirected) hypergraphs are isomorphic
Determine whether two ordered (directed) hypergraphs are isomorphic
Evaluate the Jacobi epsilon function
Find the solution of the Josephus problem
Find the minimal spanning tree for a given set of points in Euclidean space
Give all possible ways to partition a set into a given number of subsets, ignoring order of blocks and within blocks
Calculate the Kullback–Leibler divergence between two distributions
Find the largest prime factor of a given integer
Give the greatest gap between the primes up to the argument
The logit function from probability
Display an L-system
Get a list of lucky numbers
Compute the evolution of a mobile automaton
Visualization of the evolution of a mobile automaton
Generate the rule icon for a mobile automaton
Implement the Ramanujan mock theta functions
Computes polygons, circles, compositions, and transformation functions for the tessellation of the upper half-plane by the modular group.
Convert an axiom system from modus ponens to equational form
Truncate negative numbers in the result of subtraction
Determine the cardinality for a multiset
Perform the complement operation on multisets
Compute the Dice dissimilarity of two multisets
Test whether or not one multiset is included in another multiset
Perform the intersection operation on multisets
Compute the Jaccard dissimilarity of two multisets
Perform the product operation on multisets
Compute the Sokal–Sneath dissimilarity of two multisets
Perform the sum operation on multisets
Determine the support for a multiset
Get the symmetric difference of the given lists
Perform the union operation on multisets
Numerically evaluate the gradient of a function summed over the eigenvalues of a matrix, with respect to matrix parameters
Find the error in the Newton–Cotes quadrature formula
Get the abscissa–weight pairs of the elementary Newton–Cotes formula
Get the successor, in Gray code order, of a given subset
Get the next composition of an integer in canonical order
Get the next partition of an integer in reverse lexicographic order
Get the lexicographic successor of a k-subset of a list
Get the next subset of a given set in lexicographic order
Get the next permutation in lexicographic order
Plot a nondeterministic finite automaton
Simulate the behavior of a nondeterministic finite automaton
Find the numerical approximation for the inverse Laplace transform
Compute the normal surface of a curve
Get the subset of a list for a given index
Compute the nullity of a matrix
Get the ordered tuple with the given index and length
Give the index of an ordered tuple
Get Dyson's crank of an integer partition
Construct the corresponding partition, given a Frobenius symbol
The largest part minus the number of parts of a partition
Display a given number of rows in Pascal's triangle
Make plots of Penrose tiles
Test whether a permutation equals its inverse
Get a list of powers of the golden ratio which sum to a given integer
Get the value of the Plouffe P function
Compute the Hermite decomposition of a matrix of univariate polynomials
Compute the Smith decomposition of a matrix of univariate polynomials
Compute the Popov decomposition of a matrix of univariate polynomials
Replace elements with their position of first appearance when flattened
Subdivide an interval such that the ratio of subsequent elements is constant
Give the remainder on division of a power tower expression
Test if a certificate can be used for ascertaining the primality or compositeness of a number
Get the set of primitive nth roots of unity
Certify a number as provably prime
Compute the quadratic residues of an integer
A quantum cellular automaton model that evolves the tensor product of a collection of initial qubits using arbitrary compositions of unitary operators for a finite number of steps
Represent a quaternion object
Plot an array of digits, allowing them to be ragged on the left
Find a rational interpolation of a function
Find a near minimal set of marks for an integer length ruler so that all smaller integer distances are measurable
Plot Riemann surfaces of compositions of elementary functions
Compute a rolling curve
Compute properties of the row space of a matrix
Conduct a runs up–based randomness test on a sequence of random reals between 0 and 1
List equations for Runge–Kutta methods
Conduct a randomness test on a sequence of random reals between 0 and 1 using run lengths of increasing subsequences
Cellular automaton evolution with the order of each cell update specified
Compute the evolution of a sequential substitution system
Visualization of the evolution of a sequential substitution system
Generate the rule icon for a sequential substitution system
Conduct an empirically derived test that assesses randomness using the frequencies of serial combinations of 0s and 1s
Get the pairs of primes that differ by 6
Get the measure of a simplex or simplicial complex
Total number of smallest parts in the partitions of a positive integer
Find a small solution to a system of linear equations over the integers
Use a discrete cosine transform–based method to test the randomness of a sequence of random reals
Get the standard ordering of the desired index
Get the index of a list of integers in standard order
Get the standard simplex for a specified dimension
Construct a stem-and-leaf diagram
Generate the zero-free compositions of a positive integer
Estimate the full size of a set given the number of distinct results in a sample
Get the evolution of a symbolic system
Compute the evolution of a tag system
Generate the rule icon for a tag system
Compute the tangent developable surface of a curve
Transform components of tensors with arbitrary rank with regard to their transformation behavior under any given mapping
Given a metric, convert between covariant and contravariant components of a tensor
Get the inversion vector of a permutation written as a list
Get the integers from 1 to n that have no common proper factor with n
Convert an expression involving Dot and Tr into an equivalent expression using TensorContract
Encrypt with Tupper’s self-referential formula
Decrypt with Tupper’s self-referential formula
Get the pairs of primes that differ by 2
Starting with the third term, give the least integer expressible uniquely as the sum of two distinct earlier terms
Check if the given graph coloring is valid
Calculate the variance of a list along with its uncertainty
Test whether an integer is a wasteful number
Give the 0–1 list that indicates the unique nonconsecutive Fibonacci numbers that sum to the non-negative integer input